Question

ok i need help with this word problem

"The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number."
im pretty sure i have it but i dont know what variable to use for the 2 digit number

Answer 1

Le the digits be x and y. Hence the original number is = 10x + y.

Since the digits add up to 8. Hence, x + y = 8

Again adding 16 to the original number we get - 10x + y + 16

This number is 3 times of the original number reversed 3(10y + x)

Hence, 10x + y + 16 = 3 (10y +x)

=> 7x - 29y = -16

Replacing y = 8 - x, we have

7x - 29(8 - x) = -16 => x = 6, hence y = 8 - 6 = 2

Hence the original number is 10 * 6 + 2 = 62

Answer 2

where did the -10 come from?

Answer 3

no no :) that is not -10, I just written "we get -' the number actually is 10x + y + 16

Answer 4

haha sorry then where did the 10 come from

Answer 5

x is the ten's digit. It's value is 10x

Answer 6

ohh ok thanks guys

Answer 7

im gonna have more of these coming so get ready haha:)